Savitzky-Golay-Filter

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Savitzky-Golay-Filter

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Consists of Matlab Algorithms necessary for denoising ECG signals.

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# Savitzky-Golay-Filter
Consists of Matlab Algorithms necessary for denoising ECG signals.

Introduction
	 Real-time signals are often corrupted with noise. Noise can be moving or stationary. In this paper we aim to smoothen the Noisy Signals to a Smooth signal. We try to employ filters to smoothen the data points and compute the approximate clean signal. The filter is based local least-square polynomial approximation and was formulated by the duo,Savitzky and Golay,hence is the name of these filters.Signal denoising is vital for further signal processing. 
	 These Savitzky-Golay Filters (SG Filters) are finite impulse response,low pass, Digital filters. The algorithms expounded in [2] are verified for ECG signals taken from physio-net database .The duo further proved the fact that local least squares polynomial regression is equal to a discrete convolution with a fixed impulse response assuming that data samples are symmetric about the origin. Savitzky and Golay have shown that the shape of the signal is preserved and significant noise reduction is observed.SG filters are characterized by the Order(N) and Length of the filter(M). By choosing appropriate Length and Order, noise can be eliminated to a large extent.In this context we assume the clean signal s[n],noise w[n] which is Additive White Gaussian of zero mean and standard deviation of $\sigma$.

Savitzky-Golay-Filter

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